Triebel-Lizorkin spaces with non-doubling measures

Yongsheng Han, and Dachun Yang. "Triebel-Lizorkin spaces with non-doubling measures." Studia Mathematica 162.2 (2004): 105-140. <http://eudml.org/doc/285236>.

@article{YongshengHan2004,
abstract = {Suppose that μ is a Radon measure on $ℝ^\{d\}$, which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces $Ḟ^\{s\}_\{pq\}(μ)$ for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality of Fefferman and Stein and is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are given.},
author = {Yongsheng Han, Dachun Yang},
journal = {Studia Mathematica},
keywords = {non-doubling measure; Triebel-Lizorkin space; Calderón-type reproducing formula; approximation to the identity; Riesz potential; lifting property; dual space},
language = {eng},
number = {2},
pages = {105-140},
title = {Triebel-Lizorkin spaces with non-doubling measures},
url = {http://eudml.org/doc/285236},
volume = {162},
year = {2004},
}

TY - JOUR
AU - Yongsheng Han
AU - Dachun Yang
TI - Triebel-Lizorkin spaces with non-doubling measures
JO - Studia Mathematica
PY - 2004
VL - 162
IS - 2
SP - 105
EP - 140
AB - Suppose that μ is a Radon measure on $ℝ^{d}$, which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces $Ḟ^{s}_{pq}(μ)$ for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality of Fefferman and Stein and is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are given.
LA - eng
KW - non-doubling measure; Triebel-Lizorkin space; Calderón-type reproducing formula; approximation to the identity; Riesz potential; lifting property; dual space
UR - http://eudml.org/doc/285236
ER -